Question #0516f

1 Answer
Sean
Jan 4, 2018

#A=21#

Explanation:

.

Let's see the graph of this area:

enter image source here

#y=x^2-2x+5#

This parabola is shown in purple.

#y=-x^2+2x-2#

This parabola is shown in red.

#x=0# is the #y#-axis and is shown in blue.

#x=3# is the green vertical line.

The area we need to find is bound by the two parabolas, the #y#-axis and the green line. I have colored this area in pink.

To calculate this area, we subtract the function of the red parabola from the function of the purple parabola, take its integral, and evaluate it from #0# to #3#:

#A=int_0^3[x^2-2x+5-(-x^2+2x-2)]dx#

#A=int_0^3(x^2-2x+5+x^2-2x+2)dx#

#A=int_0^3(2x^2-4x+7)dx=(2/3x^3-2x^2+7x)_0^3#

#A=2/3(3)^3-2(3)^2+7(3)-0=18-18+21=21#

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